Electromotive Force Revisited When we say something has energy, it can do work Electric potential is the potential energy per unit charge: the amount of work doable per unit charge The amount of work a device can supply per unit charge is the electromotive force (EMF) Denoted E Ch. 31

Motional EMF Suppose you have the following circuit in the presence of a magnetic field Charges inside the cylinder Now let cylinder move Moving charges inside conductor feel force Force transport charges – it is capable of doing work This force is like a battery - it produces EMF v L B v  B v is the rate of change of the width W We can relate this to the change in magnetic flux W

Lenz’s Law Force on charges in rod move them upward gives counter-clockwise current. Counter clockwise current increases flux through loop The magnetic field of an induced current opposes the change that produced it.

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Concept questions Flux into screen is decreasing. Want to increase it to oppose that. A wire, initially carrying no current, has a radius that starts decreasing at t = 0. As it shrinks, which way does current begin to flow in the loop? A) ClockwiseB) Counter-clockwiseC) No current D) Insufficient information

Lenz’s Law As the wire shrunk, the magnetic flux decreased But the wire acquired a current, which tried to increase it The induced current in a loop is in the direction that opposes the change in magnetic flux through the area enclosed by the loop Current loops resist change Move loop to the right Current flows to maintain B-field Current dies away Move loop to the left Current flows to kill B-field Current dies away

Power and Motional EMF Resistor feels a voltage – current flows v L B To get it to move, you must oppose this force You are doing work The power dissipated in the resistor matches the mechanical power you must put in to move the rod R Where does the power come from? Current is in a magnetic field F

Electric Fields from Faraday Magnet We can generate electromotive force – EMF – by moving the loop in and out of magnetic field Can we generate it by moving the magnet? Faraday’s Law works whether the wire is moving or the B-field is changing* How can there be an EMF in the wire in this case? Charges aren’t moving, so it can’t be magnetic fields Electric fields must be produced by the changing B-field! The EMF is caused by an electric field that points around the loop

Solve on Board

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Eddy Currents As magnet falls, some places have magnetic fields that diminish Current appears, replacing magnetic field This acts like a magnet, pulling it back up At bottom end, current appears to oppose change This repels the magnet, slowing it down What happens as I drop the magnet into the copper tube (Compare to if drop equivalent non-magnet)? A) Falls as usualB) Falls slower C) Falls fasterD) Floats constant E) Pops back up and out Current is only caused by motion of magnet If motion stops, resistance stops current If motion is small, opposition will be small It doesn’t stop, it goes slowly N S S N S N

Warmup 17

How to make an AC generator Have a background source of magnetic fields, like permanent magnets Add a loop of wire, attached to an axle that can be rotated Add “slip rings” that connect the rotating loop to outside wires A Rotate the loop at angular frequency  Magnetic flux changes with time This produces EMF To improve it, make the loop repeat many (N) times

Sample Problem A rectangular loop of wire 20 cm by 20 cm with 50 turns is rotated rapidly in a magnetic field B, so that the loop makes 60 full rotations a second. At t = 0 the loop is perpendicular to B. (a) What is the EMF generated by the loop, in terms of B at time t? (b) What B-field do we need to get a maximum voltage of 170 V? loop of wire The angle is changing constantly with time After 1/60 second, it must have gone in one full circle  The EMF is given by

Comments on Generators: The EMF generated is sinusoidal in nature (with simple designs) This is called alternating current - it is simple to produce This is actually how power is generated Generators extremely similar to motors – often you can use a single one for both Turn the axle – power is generated Feed power in – the axle turns Regenerative braking for electric or hybrid cars

Ground Fault Circuit Interrupters Fuses/circuit breakers don’t keep you from getting electrocuted But GFI’s (or GFCI’s) do Under normal use, the current on the live wire matches the current on the neutral wire Ampere’s Law tells you there is no B-field around the orange donut shape Now, imagine you touch the live wire – current path changes (for the worse) There is magnetic field around the donut Changing magnetic field means EMF in blue wire Current flows in blue wire Magnetic field produced by solenoid Switch is magnetically turned off GFCI